Correct option is A) 2, 4, 6, 8,
(A) 2, 4, 6, 8, ......
\(a_2-a_1\) \(=4-2=2\)
\(a_3-a_2\) \(=6-4=2\)
and \(a_4-a_3\) \(=8-6=2\)
\(\because\) \(a_4-a_3\) \(=a_3-a_2\) \(=a_2-a_1\) \(=2\)
\(\therefore\) 2, 4, 6, 8, ...... is an arithmetic progression.
(B) 1, 2, 4, 8, ........
\(a_2-a_1\) \(=2-1=1,\)
\(a_3-a_2\) \(=4-2=2\)
\(\because\) \(a_3-a_2\) \(\neq a_2-a_1\)
\(\therefore\) 1, 2, 4, 8, ........ will not form an A.P.
(C) 4, 9, 16, 25, .......
\(a_2-a_1\) \(=9-4=5,\)
\(a_3-a_2\) \(=16-9=7\)
\(\because\) \(a_3-a_2\) \(\neq a_2-a_1\)
\(\therefore\) 4, 9, 16, 25, ....... will not form an A.P.
(D) 3, 9, 12, 18, .........
\(a_2-a_1\) \(=9-3=6,\)
\(a_3-a_2\) \(=12-9=3\)
\(\because\) \(a_3-a_2\) \(\neq a_2-a_1\)
\(\therefore\) 3, 9, 12, 18, ......... will not form an A.P.
